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• Qualitative reasoning for earthquake resistant buildings

  L. Rotondo

  Monograph Series in Earthquake Engineering, editor A. H. Barbat (1993). MIS01

  
  

  Abstract

  Qualitative reasoning is a new field of research from artificial intelligence that derives the behavior of a model from a high-level representation of the fundamental principles of the domain, and the geometry andtopology of the model. Qualitative reasoning is useful for evaluating concepetual designs of earthquake resistant buildings because it derives values for parameters even with incomplete and imprecise knowledge about the model, which is particularly importante for the conceptual design stage.

  Abstract
  Qualitative reasoning is a new field of research from artificial intelligence that derives the behavior of a model from a high-level representation of the fundamental principles [...]

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• A stabilized formulation for incompressible elasticity using linear displacement and pressure interpolations

  M. Chiumenti, Q. Valverde, C. Agelet de Saracibar, M. Cervera

  Comput. Methods Appl. Mech. Engrg., (2002). Vol. 191 (46), pp. 5253-5264

  
  

  Abstract

  In this paper a stabilized finite element method to deal with incompressibility in solid mechanics is presented. A mixed formulation involving pressure and displacement fields is used and a continuous linear interpolation is considered for both fields. To overcome the Babuška–Brezzi condition, a stabilization technique based on the orthogonal sub-scale method is introduced. The main advantage of the method is the possibility of using linear triangular or tetrahedral finite elements, which are easy to generate for real industrial applications. Results are compared with standard Galerkin and Q1P0 mixed formulations for nearly incompressible problems in the context of linear elasticity.

  Abstract
  In this paper a stabilized finite element method to deal with incompressibility in solid mechanics is presented. A mixed formulation involving pressure and displacement fields [...]

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• Mesh objective modeling of cracks using continuous linear strain and displacement interpolations

  M. Cervera, M. Chiumenti, R. Codina

  Int. J. Numer. Meth. Engng. (2011). Vol. 87 (10), pp. 962-987

  
  

  Abstract

  The paper addresses the problem of tensile and mixed‐mode cracking within the so‐called smeared crack approach. Because lack of point‐wise convergence on stresses is deemed as the main difficulty to be overcome in the discrete problem, a (stabilized) mixed formulation with continuous linear strain and displacement interpolations is used. The necessary convergence rate can be proved for such a formulation, at least in the linear problem. Two standard local isotropic Rankine damage models with strain‐softening, differing in the definition of the damage criteria, are used as discrete constitutive model. Numerical examples demonstrate the application of the proposed formulation using linear triangular P1P1 and bilinear quadrilateral Q1Q1 mixed elements. The results obtained do not suffer from spurious mesh‐bias dependence without the use of auxiliary tracking techniques.

  Abstract
  The paper addresses the problem of tensile and mixed‐mode cracking within the so‐called smeared crack approach. Because lack of point‐wise convergence on stresses is [...]

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• A smeared‐embedded mesh‐corrected damage model for tensile cracking

  M. Cervera

  Int. J. Numer. Meth. Engng. (2008). Vol. 76 (12), pp. 1930-1954

  
  

  Abstract

  Traditional smeared orthotropic models display an unacceptable dependence of the solution on the alignment of the mesh, which usually manifests as stress locking. A solution for this drawback is proposed in this paper by adopting the concept of embedded inelastic strains, rather than displacement jumps, and by linking the structure of the inelastic strain to the geometry of the cracked element. The resulting model, applicable to linear 3‐noded triangles, is formulated as a non‐symmetric orthotropic local damage constitutive model, with the softening modulus regularized according to the material fracture energy and the element size. Analytical and numerical results show that this approach is effective in removing the locking problem as well as efficient from the computational point of view.

  Abstract
  Traditional smeared orthotropic models display an unacceptable dependence of the solution on the alignment of the mesh, which usually manifests as stress locking. A solution [...]

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• Thermo‐mechanical analysis of industrial solidification processes

  M. Cervera, C. Agelet de Saracibar, M. Chiumenti

  Int. J. Numer. Meth. Engng. (1999). Vol. 46 (9), pp. 1575-1591

  
  

  Abstract

  The paper presents an up‐to‐date finite element numerical model for fully coupled thermo‐mechanical problems, focussing in the simulation of solidification processes of industrial metal parts. The proposed constitutive model is defined by a thermo‐visco‐elasto‐(visco)plastic free energy function which includes a contribution for thermal multiphase changes. Mechanical and thermal properties are assumed to be temperature‐dependent, and viscous‐like strains are introduced to account for the variation of the elastic moduli during the cooling process. The continuous transition between the initial fluid‐like and the final solid‐like behaviour of the part is modelled by considering separate viscous and elasto‐plastic responses as a function of the solid fraction. Thermo‐mechanical contact conditions between the mould and the part are specifically considered, assuming that the heat flux is a function of the normal pressure and the thermal and mechanical gaps. A fractional step method arising from an operator split of the governing equations is used to solve the non‐linear coupled system of equations, leading to a staggered product formula solution algorithm suitable for large‐scale computations. Representative simulations of industrial solidification processes are shown, and comparison of computed results using the proposed model with available experimental data is given.

  Abstract
  The paper presents an up‐to‐date finite element numerical model for fully coupled thermo‐mechanical problems, focussing in the simulation of solidification processes [...]

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• Estudio de la distribución transitoria del gas en redes urbanas por el método de los elementos finitos

  B. Suárez, E. Oñate

  Anales de Ingeniería Mecánica (1984). Vol. 2 (1), pp. 59-68

  
  

  Abstract

  Se representa una formulación por elementos finitos que permite simular la distribución transitoria de presiones y caudales del gas en redes urbanas. Esta formulación, que parte de las ecuaciones básicas que proporciona la mecánica de fluidos para la circulación de un gas en régimen variable por conductos cilíndricos, utiliza elementos finitos unidimensionales parabólicos para discretizar los distintos tramos de la red y un esquema paso a paso de integración en el tiempo que supone una variación lineal de la presión del gas en cada intervalo de tiempo. La formulación se aplica al caso real de la red media presión de la ciudad de Barcelona utilizando algunos resultados experimentales para confirmar su eficiencia y aproximación. 

  Abstract
  Se representa una formulación por elementos finitos que permite simular la distribución transitoria de presiones y caudales del gas en redes urbanas. Esta formulación, [...]

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• Foreword: special issue on particles finite element method in multi-physics problems

  S. Idelsohn

  Comp. Part. Mech (2017). Vol. 4 (3), pp. 249-249

  
  

  Abstract

  Particle-based methods in which each material particle is followed in a Lagrangian manner have been used successfully in the last years for different applications. One of the latest evolution of particle-based methods is the Particle Finite Element Method (PFEM). The PFEM combines the particle precept with the FEM shape functions using an auxiliary FE mesh. This mesh may be quickly rebuilt at each time step (PFEM with moving mesh) or may be a fixed mesh (PFEM with fixed mesh). In the last case, the results from the Lagrangian particles are projected at each time iteration on a fixed mesh. The idea of combining FMs with moving particles was originally used in the so-called Particle in Cell method and later in an extension called the Material Point Method (MPM), which uses an FE background mesh. Despite that both PFEM and MPM employ a fixed FE mesh and a set of Lagrangian particles, there are important differences in the way the particles are employed; in the MPM, all computations are performed on the mesh, while in the PFEM, the aim is to calculate as much as possible on the particles, leaving small corrections to be performed on the mesh. Furthermore, the most important difference is that in PFEM, the particles do not represent a fixed amount of mass but rather material points that transport only intrinsic properties. This allows using a variable number of particles and therefore simplifying refinement. The PFEM has been successfully used to solve the Navier–Stokes equations and fluid–structure interaction problems as well as solid mechanics problems. The advantages of the PFEM concerning the tracking of internal interfaces have also been explored and used to solve multi-fluid flows. The possibility to use PFEM to solve nonlinear problems with large time-steps in order to obtain an accurate and fast solution was also successfully presented for the solution of the homogeneous incompressible Navier–Stokes equations. This new strategy was named PFEM second generation (PFEM-2). The enhanced PFEM-2 version to solve multi-phase problems, preserves the large time-step goodnesses of the single-phase strategy, also includes enrichment strategies to capture discontinuities in the pressure gradient, i.e., pressure kinks. This special issue is a collection of nine technical papers presenting the state-of-the-art in modeling and simulations of solid and fluid mechanics problems at different scales involving the Particle Finite Element Method as well in his original version (PFEM) as in his new upgrade (PFEM-2).

  Abstract
  Particle-based methods in which each material particle is followed in a Lagrangian manner have been used successfully in the last years for different applications. One [...]

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• On load interaction in the non linear buckling analysis of cylindrical shells

  L. Godoy, S. Idelsohn, E. Barbero

  Advances in Engineering Software and Workstations (1991). Vol. 13 (1), pp. 46-50

  
  

  Abstract

  The elastic stability of shells or shell-like structures under two independent load parameters is considered. One of the loads is associated to a limit point form of buckling, whereas the second is a bifurcation. A simple one degree of freedom mechanical system is first investigated, for which an analytical solution is possible. Next, a cylindrical shell under the combined action of axial load and localised lateral pressure is studied via a non linear, two-dimensional, finite element discretization. It is shown that both problems display the same general behaviour, with a stability boundary in the load space which is convex towards the region of stability. The results show the need of performing a full non-linear analysis to evaluate the stability boundary for the class of interaction problems considered.

  Abstract
  The elastic stability of shells or shell-like structures under two independent load parameters is considered. One of the loads is associated to a limit point form of buckling, [...]

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• Upwind parameters for the numerical solution of the compressible flow Euler equations

  S. Idelsohn

  Advances in Engineering Software and Workstations (1991). Vol. 13 (2), pp. 58-67

  
  

  Abstract

  The present work generalises the earlier work in which a variational principle technique was presented in order to evaluate the magnitude of upwind required to solve the compressible flow equations. The technique proposed allows the choice of nodes where upwind is required in each of the relevant equations. It is a simple and mathematically consistent way of evaluating the amount of upwind or artificial viscosity to be introduced at every node and every equation involved.

  Abstract
  The present work generalises the earlier work in which a variational principle technique was presented in order to evaluate the magnitude of upwind required to solve the compressible [...]

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• Numerical implementation of a discontinuous finite element algorithm for phase-change problems

  M. Storti, L. Crivelli, S. Idelsohn

  Advances in Engineering Software (1987). Vol. 9 (2), pp. 66-73

  
  

  Abstract

  This paper is devoted to the numerical solution of phase-change problems in two dimensions. The technique of finite elements is employed. The discretization is carried out using linear isoparametric elements and special attention is given to the accurate integration of functions presenting discontinuities at arbitrarily curved interfaces. This type of function arises in a natural way when dealing with phase-change problems because the enthalpy attains a discontinuity at the phase change temperature. To integrate the discontinuous functions in the phase-changing elements a second mapping is performed from the master element onto a new one for which the interface iis a straight line. The integrals are calculated using the Gaussian technique applied to each part of the divided element, which may be triangular or quadrilateral. The discontinuous integration technique improves the behaviour of the numerical method avoiding any possible loss of latent heat due to an inaccurate evaluation of the residual vector. Some important aspects of the solution of the nonlinear system of equations are discussed and several numerical examples are presented together with the details of the computational implementation of the algorithm.

  Abstract
  This paper is devoted to the numerical solution of phase-change problems in two dimensions. The technique of finite elements is employed. The discretization is carried out [...]

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